$256$ discrete values between $0$ and $255$, every value is represented.
For the metrics the ouput $y \in [-1,1]$ was not trasformed nor rounded.
absolute $\epsilon$-accuracy
diff <- |target_set - predicted_set| // pixelwise difference stored as (10000, 784)
accu <- 0 // accumulator
loop elem in diff // for each element in diff i.e. for each number, image (784,)
accu <- |{i ∈ elem : elem < ε }| / 784 //count how many elements are > ε and average over pixels, i.e. divide by 784
accu <- accu/10000 // Average over examples in image set
absolute $\epsilon$-outliers
diff <- |target_set - predicted_set| // pixelwise difference stored as (10000, 784)
accu <- 0 // accumulator
loop elem in diff // for each element in diff i.e. for each number, image (784,)
accu <- |{i ∈ elem : elem > ε }| / 784 //count how many elements are > ε and average over pixels, i.e. divide by 784
accu <- accu/10000 // Average over examples in image set
squared $\epsilon$-accuracy
diff <- (target_set - predicted_set)^2 // pixelwise difference stored as (10000, 784)
accu <- 0 // accumulator
loop elem in diff // for each element in diff i.e. for each number, image (784,)
accu <- |{i ∈ elem : elem < ε }| / 784 //count how many elements are > ε and average over pixels, i.e. divide by 784
accu <- accu/10000 // Average over examples in image set
squared $\epsilon$-outliers
diff <- (target_set - predicted_set)^2 // pixelwise difference stored as (10000, 784)
accu <- 0 // accumulator
loop elem in diff // for each element in diff i.e. for each number, image (784,)
accu <- |{i ∈ elem : elem > ε }| / 784 //count how many elements are > ε and average over pixels, i.e. divide by 784
accu <- accu/10000 // Average over examples in image set
$\operatorname{mse} =\frac{1}{m} \sum_{j=1}^{m} \frac{1}{n} (Y_j-\hat{Y_j})^2 = \frac{1}{m} \sum_{j=1}^{m} \frac{1}{n} \sum_{i=1}^{n} (y_i-\hat{y_i})^2$
where:
$\operatorname{mae} =\frac{1}{m} \sum_{j=1}^{m} \frac{1}{n} |Y_j-\hat{Y_j}| = \frac{1}{m} \sum_{j=1}^{m} \frac{1}{n} \sum_{i=1}^{n} |y_i-\hat{y_i}|$
where:
Average over: the maximal absolute diference between pixels in each example. i.e. $\underset{i}{mean}(max(|\mathbb{Y}_i-\mathbb{\hat{Y}}_i|))$
Maximum over: the maximal absolute diference between pixels in each example. i.e. $max(max(|\mathbb{Y}_i-\mathbb{\hat{Y}}_i|))$
where:
absolute $\epsilon$-error
diff <- |target_set - predicted_set| // pixelwise difference stored as (10000, 784)
diff <- flatten dif // becomes vector of 10000 * 784 different error values
diff <- filter all elem < ε // all elements smallet than ε are taken out of the list
create histogram(diff, bin_size)
squared $\epsilon$-error
diff <- (target_set - predicted_set)^2 // pixelwise difference stored as (10000, 784)
diff <- flatten dif // becomes vector of 10000 * 784 different error values
diff <- filter all elem < ε // all elements smallet than ε are taken out of the list
create histogram(diff, bin_size)